{
  "id": 5943,
  "curve_key": "823342670807024408288746192777825:-24156964236706671167257208931294350391471982244113",
  "ainvs": [
    "1",
    "0",
    "0",
    "-17152972308479675172682212349538",
    "27959449348040127236392595741617752266611913284"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 227.41731435286337,
  "faltings_height": 16.851667101901143,
  "conductor": "5903198543007601946565130564454539165491166",
  "bad_primes": [
    "2",
    "7",
    "59",
    "79",
    "97",
    "109",
    "113",
    "139",
    "197",
    "439",
    "2971",
    "9013",
    "19183",
    "27932188183"
  ],
  "discriminant": "-14710973119242628176320402632511891083674776519225465481973671129517588257964483878608277864448",
  "regulator": "75972060907318.242913330863798295363358005778247889218988806194",
  "points": [
    [
      "20539600825290070651837335636/12035716378009",
      "2525058506779981229911078024308783949119446/41754945151556857277"
    ],
    [
      "-41399680677249882213522716/26598021921",
      "-978538156932193382597263570783605161618/4337844797073969"
    ],
    [
      "747899952835536827006436/264745441",
      "-194915260627264543275129060470884142/4307673070511"
    ],
    [
      "-10391295008000611276192096/2342656801",
      "-14683962072822191517449281811158816562/113386931825201"
    ],
    [
      "1057685556952249154160/36481",
      "34065287792356783764741488456978/6967871"
    ],
    [
      "-2627907716427300687554804229749530556/591602927506427215369",
      "1848682999402255086309663294250858429314322966967739002/14389492315924567628261474072347"
    ],
    [
      "-16726739681839195799195244/8642491225",
      "186545237951731219091775656010001957526/803449196732125"
    ],
    [
      "688395772704372794115460/390576169",
      "436805037025293807343072085530232986/7718956827947"
    ],
    [
      "17701791904830528222889068910246/5505348397861225",
      "-31769830414024857411005858962406216472600270024/408486033111701097692875"
    ],
    [
      "89190353066388821544303484/30693988809",
      "-276922997956693436479892745875938960882/5377494757370373"
    ],
    [
      "2210300375158626992184059948356/1005100308802489",
      "941678051094534326371433526856484045588399414/31865013706763199156013"
    ],
    [
      "5230646034459508468666/2608225",
      "169835796294895038225778956068316/4212283375"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = 2383/632 for the rank-5 fibration of X163 given by y^2 + (9T^2 - 6T + 244)xy + (13T - 90)(22T - 15)(5T + 6)(4T + 15)y = x^3 mentioned in the curve#4645",
  "created_at": "2026-10-26 01:53:12",
  "updated_at": "2026-10-26 01:53:12"
}